In: Statistics and Probability
If n =400 and X = 140, construct a 99% confidence interval estimate for the population proportion.
? ≤ π ≤ ?
(Round to four decimal places as needed.)
Solution :
Given that,
Point estimate = sample proportion =
= x / n = 140 / 400 = 0.350
1 -
= 1 - 0.350 = 0.65
Z/2
= 2.576
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 2.576 * (((0.350
* 0.65) / 400)
Margin of error = E = 0.0614
A 99% confidence interval for population proportion p is ,
- E
π
+ E
0.350 - 0.0614
π
0.350 + 0.0614
0.2886
π
0.4114